There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arcsin(ln(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(ln(x))\right)}{dx}\\=&(\frac{(\frac{1}{(x)})}{((1 - (ln(x))^{2})^{\frac{1}{2}})})\\=&\frac{1}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}})}{x} + \frac{-1}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{2}}\\=&\frac{ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{2}} - \frac{1}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{2}} - \frac{1}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{2}}\right)}{dx}\\=&\frac{(\frac{\frac{-3}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}})ln(x)}{x^{2}} + \frac{-2ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}} + \frac{1}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{2}(x)} - \frac{(\frac{\frac{-1}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}})}{x^{2}} - \frac{-2}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{3}}\\=&\frac{3ln^{2}(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{3}} - \frac{3ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}} + \frac{1}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}} + \frac{2}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3ln^{2}(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{3}} - \frac{3ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}} + \frac{1}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}} + \frac{2}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{3}}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{7}{2}}})ln^{2}(x)}{x^{3}} + \frac{3*-3ln^{2}(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{4}} + \frac{3*2ln(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{3}(x)} - \frac{3(\frac{\frac{-3}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}})ln(x)}{x^{3}} - \frac{3*-3ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{4}} - \frac{3}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{3}(x)} + \frac{(\frac{\frac{-3}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}})}{x^{3}} + \frac{-3}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{4}} + \frac{2(\frac{\frac{-1}{2}(\frac{-2ln(x)}{(x)} + 0)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}})}{x^{3}} + \frac{2*-3}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{4}}\\=&\frac{15ln^{3}(x)}{(-ln^{2}(x) + 1)^{\frac{7}{2}}x^{4}} - \frac{18ln^{2}(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{4}} + \frac{9ln(x)}{(-ln^{2}(x) + 1)^{\frac{5}{2}}x^{4}} + \frac{11ln(x)}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{4}} - \frac{6}{(-ln^{2}(x) + 1)^{\frac{3}{2}}x^{4}} - \frac{6}{(-ln^{2}(x) + 1)^{\frac{1}{2}}x^{4}}\\ \end{split}\end{equation} \]

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